Why antenna height should be at least l/4

For efficient transmission of the signal, it is said that antenna height should be at least quarter signal wavelength(λ/4)?

there must be reason behind this or this had been concluded from experiments?

That particular length only it is resonant.

Is it antenna structure height or is it total antenna height above ground that should have a height of lamda/4?

Increased antenna height is often positive for best horizontal transmission results.
Minimum natural antenna size for a vertical dipole at resonance is lambda/2.
From that can the conclusion be that best height above ground must be at least as high as the antenna structure (lamda/2) and higher antenna position is always better but that is a small part of the truth.
How height affects the antenna depends on what type of antenna it is. A few examples:

A quarter wave vertical monopole should be placed directly at ground plane as its virtual part is mirrored in the ground.
Omnidirectional antenna types with low horizontal radiation lob angel need by design a certain height as in general lower antenna height increases lob angel. Horizontal directive antennas must have enough height so that its Fresnel zone not is affected by ground obstacles.
Attenuation between two communicating antennas is less if it is free line of sight. Increased height can improve this if it is horizontal communication.
For ground to satellite communication is a low satellite orbit height an advantage if distance between TX-RX antennas becomes less but can be at cost of less earth coverage.
Height above ground is an impedance factor for many antenna types, therefore do some antennas requires a certain height for best impedance matching. For patch antennas can that height be as low as lambda/10 or less.

Conclusion is that best antenna height above ground depends on antenna design and actual situation.

May be i'll go simple.......Coz ground on which we live is a big antenna and if your transmission wavelength is say..5 for ex and if you install the antenna at say 4 the transmission will sink and transmission part will be reduced. So it is suggested that the transmission antenna is ATLEAST 1/4 wavelenght above the ground level. More the better.

i have started first course in Electronic communication

and it is mentioned there in "KENNEDY" book in introduction chapter

I suggest you read this article: **broken link removed**
although It's about microstrip antenna, it cleared my understanding alot. Especially picture about phase/waves.
Also maybe search something about radiating and non-radiating edges.